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Algebra : Volume II: Fields with Structure, Algebras and Advanced Topics / by Falko Lorenz
(Universitext. ISSN:21916675)
版 | 1st ed. 2008. |
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出版者 | New York, NY : Springer New York : Imprint: Springer |
出版年 | 2008 |
本文言語 | 英語 |
大きさ | X, 340 p : online resource |
著者標目 | *Lorenz, Falko author SpringerLink (Online service) |
件 名 | LCSH:Algebra LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebras, Linear LCSH:Number theory FREE:Algebra FREE:Commutative Rings and Algebras FREE:Field Theory and Polynomials FREE:Linear Algebra FREE:Number Theory |
一般注記 | Ordered Fields and Real Fields -- Hilbert's Seventeenth Problem and the Real Nullstellensatz -- Orders and Quadratic Forms -- Absolute Values on Fields -- Residue Class Degree and Ramification Index -- Local Fields -- Witt Vectors -- The Tsen Rank of a Field -- Fundamentals of Modules -- Wedderburn Theory -- Crossed Products -- The Brauer Group of a Local Field -- Local Class Field Theory -- Semisimple Representations of Finite Groups -- The Schur Group of a Field The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews HTTP:URL=https://doi.org/10.1007/978-0-387-72488-1 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780387724881 |
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EB00226774 |
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※2017年9月4日以降